US President Donald Trump has lashed out at two American pro sports teams that are considering name changes amid a national reckoning about racial injustice and inequality.

“They name teams out of STRENGTH, not weakness, but now the Washington Redskins & Cleveland Indians, two fabled sports franchises, look like they are going to be changing their names in order to be politically correct,” he tweeted on Monday (US time).

Mr Trump also took aim at former presidential candidate Elizabeth Warren, saying, “Indians, like Elizabeth Warren, must be very angry right now!”.

He has repeatedly mocked Ms Warren for claiming Native American heritage, derisively calling her “Pocahontas”.

In a later tweet, Mr Trump demanded black NASCAR driver Bubba Wallace apologise for the “hoax” about a noose being found in his team garage.

“Has Bubba Wallace apologised to all of those great NASCAR drivers and officials who came to his aid, stood by his side, and were willing to sacrifice everything for him, only to find out that the whole thing was just another hoax?” he wrote.

Wallace responded to Mr Trump’s tweet with a message urging his 463,000 Twitter followers to choose “love over hate”.

“Love should come naturally as people are taught to hate,” he wrote.

“Even when it’s hate from the POTUS.”

Tweet from @BubbaWallace

On Friday, the NFL’s Redskins said that they had begun a “thorough review” of their name, which has been considered offensive by Native American groups for decades.

The Redskins’ decision came after FedEx, which paid $US205 million ($A295 million) for naming rights to the team’s stadium, and other corporate partners called for the team to change its nickname.

Hours later, the Indians Major League Baseball team said that it, too, would review its long-debated name.

“We are committed to making a positive impact in our community and embrace our responsibility to advance social justice and equality,” the team said in a statement.

Tweet from @realDonaldTrump

On Sunday, Indians manager Terry Francona said he approved of the team’s decision, saying it was “time to move forward”.

Cleveland All-Star shortstop Francisco Lindor is also in favour of the Indians changing their nickname, which they’ve had since 1915.

“I’m open to listening to the change of names,” Lindor said on Monday.

“I know society is shifting and we are due for some change. So along those guidelines, yeah, I’m open for a change in name if it’s going to bring love and happiness and more peace to the world.”

Mr Trump has spent the past few days stoking divisions and exploiting racial tensions, accusing protesters who have pushed for racial justice of engaging in a “merciless campaign to wipe out our history.”

Earlier on Monday he lashed out at NASCAR and wrongly accused the sport’s only full-time African American driver of perpetrating “a hoax” when a crew member found a noose in the team garage stall.

In 2013, Mr Trump tweeted that then-president Barack Obama “should not be telling the Washington Redskins to change their name” because “our country has far bigger problems! FOCUS on them, not nonsense.”